As Germany moves to ease restrictions under the pandemic, its public health institute said the country’s rate of coronavirus spread had dropped below a crucial threshold, a sign that the contagion was coming under control.

On average, each infected person is spreading the virus to 0.7 other people, officials said. That means that fewer people are catching the virus than are getting over it.

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As long as the figure stays below one, the number of active cases is declining, and the burden on the health care system is easing.

“Since April 12, we have recorded more recoveries than new infections,” Jens Spahn, Germany’s health minister, said at a news conference on Friday. “That is an important and encouraging development.”

Scientists around the world have estimated that without social distancing, quarantines of the ill and other precautions, each person with the new virus would give it to about two others — a formula for exponential growth.

This week, Chancellor Angela Merkel announced the first steps to ease restrictions, allowing some stores to reopen on Monday and high school students to return to classrooms to prepare for or take exams. The eastern state of Saxony is requiring people who go out in public to cover their noses and mouths either with masks or a shawl.

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The lower infection rate does not mean that Germans can return to their pre-coronavirus lifestyles, said Lothar Wieler, president of the Robert Koch Institute, the government’s public health and epidemiology center.

He cautioned that in some parts of Germany, the infection rate remained much higher, and stressed that the rate is only one point in a range of data being continually assessed to make decisions on regulation of public life.

“This virus is in our country, and it will remain in our country,” Dr. Wieler said. And the situation, he said, “can change at any time.”

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